Unit Rate as the Constant of proportionality

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7.RP.2 Recognize and represent proportional relationships between quantities.b. Identify the constant of proportionality (unit rate) in tables, graphs,

equations, diagrams, and verbal descriptions of proportional relationships.c. Represent proportional relationships by equations. For example, if total

cost, t, is proportional to the number, n, of items purchased at a constant price, p, the relationship between the total cost and the number of items can be expressed as t = pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1, r), where r is the unit rate.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.a. Solve word problems leading to equations of the form px + q = r and p(x +

q) = r where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54cm. Its length is 6cm. What is its width?

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l Students identify the same value relating the measures of x and the measures of y in a proportional relationship as the constant of proportionality and recognize it as the unit rate in the context of a given situation.

Students find and interpret the constant of proportionality within the contexts of problems.

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#48Spiral Review #13

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Unit Rate as the Constant of proportionality

National Forest Deer Population in Danger?

Wildlife conservationists are concerned that the deer population might not be constant across the National Forest. The scientists found that there were 144 deer in a 16 square mile area of the forest. In another part of the forest, conservationists counted 117 deer in a 13 square mile area. Yet a third conservationist counted 216 deer in a 24 square mile plot of the forest. Do the conservationists need to be worried?

Make a chart to organize the information above.

From this situation, is square miles proportional to the number of deer?

The unit rate of deer per 1 square mile is ___.

Constant of Proportionality: k = ___.

Use the unit rate of deer per square mile to determine how many deer will there be for every 207 square miles?

Use the unit rate to determine the number of square miles in which you would find 486 deer.

Unit Rate as the Constant of proportionality

French Class Cooking

Suzette and Margo want to prepare crêpes for all of the students in their French class. A recipe makes 20 crêpes with a certain amount of flour, milk, and 2 eggs. The girls already know that they have plenty of flour and milk to make 50 crêpes, but they need to determine the number of eggs they will need of the recipe because they are not sure they have enough.

Consider the amount of eggs necessary to make the crêpes, what is the constant of proportionality?

What does the constant of proportionality mean in the context of this problem?

How many eggs are needed to make 50 crêpes?

You Need WHAT???

Brandon came home from school and informed his mother that he had volunteered to make cookies for his entire grade level. He needs 3 cookies for each of the 96 students in the 7th grade. Unfortunately, he needs the cookies the very next day! Brandon and his mother determined that they can fit 36 cookies on two cookie sheets.

Is the number of cookies proportional to the number of cookie sheets used in baking? Create a table that shows data for the number of sheets needed for the total number of cookies baked.

Explain the meaning of the constant of proportionality in this problem.

It takes 2 hours to bake 8 sheets of cookies. If Brandon and his mother begin baking at 4pm, when will they finish baking the cookies?

Unit Rate as the Constant of proportionality

Name: __________________________________ Date: ______Pre-Algebra Exit Ticket

Bananas are $0.59/pound. a. What is the constant of proportionality, k?

b. How much will 25 pounds of bananas cost?

Name: __________________________________ Date: ______Pre-Algebra Exit Ticket

Bananas are $0.59/pound. c. What is the constant of proportionality, k?

d. How much will 25 pounds of bananas cost?

Name: _______________________________________ Date: _____

Unit Rate as the Constant of proportionality

Pre-Algebra HW #48

1. Each school year, the 7th graders who study Life Science participate in a special field trip to the city zoo. In 2010, the school paid $1,260 for 84 students to enter the zoo. In 2011, the school paid $1,050 for 70 students to enter the zoo. In 2012, the school paid $1,395 for 93 students to enter the zoo.

Is the price the school pays for each year in entrance fees proportional to the number of students entering the zoo? (Make a unit rate table.)

Explain why or why not.

Identify the constant of proportionality and explain what it means in the context of this situation.

What would the school pay if 120 students entered the zoo?

How many students would enter the zoo if the school paid $1,425?

Lesson Summary

If a proportional relationship is described by the set of ordered pairs that satisfies the equation y = kx, where k is a constant, then k is called the constant of proportionality.

Unit Rate as the Constant of proportionality

Review:2.

The temperature in St. Cloud, Minnesota, was -4°F on January 27 and 9°F on January 28.

Part A: On the number line below, plot the temperatures for January 27 and January 28. Be sure to label both points with the appropriate date.

Part B: How many degrees warmer was it on January 28 than on January 27?